Speaker

:

Dr. D. Yogeshwaran

Subject Area

:

Mathematics

Venue

:

Lecture Hall - I, Dept of Mathematics

Time

:

4.00 pm

Date  

:

January 4 and 7,2008 (Friday & Monday)

Title

:

Directionally convex ordering of random measures, shot-noise fields and some applications to wireless networks.

In the standard stochastic geometric setting, wireless networks can be modeled as point processes and their performances as certain mean functionals of the point process. Obtaining closed form expressions of such functionals is not easy for a general class of point processes. This motivates a comparative study. We study comparison of one such class of mean functionals - the additive and extremal shot-noise fields - which arise naturally in modeling of wireless networks, as ingredients of the so called Signal-to-Interference-Noise-Ratio.
To analyze them more rigorously, we make a comparative study of similar point processes (i.e, point processes with same number of points on a average but differing variances). More generally, we formulate a notion of comparison of random measures (measure-valued random variables) with point processes being nothing but random counting measures. Extensively using the theory of stochastic ordering, we show implications of this comparison on attraction or repulsion of points, shot-noise fields etc. The interesting examples are the ones that enable comparison of a clustered point processes with a homogeneous point process. Such examples shall be discussed. This is an on-going joint work with Francois Baccelli and Bartek Blaszczyszyn.